Compensated rotary mechanism construction



Sept. 3', 1963 M. BENTELE ETAL 3, 02,492

COMPENSATED ROTARY MECHANISM CONSTRUCTION Filed May 10, 1961 6Sheets-Sheet l F G- I- m 52 I 42 A? 5a a 2a) 34 F I G. 2-

INVENTORS MAX BENTELE EROLD PIERCE BY CHARLES .JoNEs ATTORN EYS Sept. 3,1963 M. BENTELE ETAL 3,102,492

COMPENSATED ROTARY MECHANISM CONSTRUCTION Filed May 10, 1961 6Sheets-Sheet 2 MAX BENTELE EROLD F. PIERCE BY CHARLES JONES ATTORN EYSSept. 3, 1963 Filed May 10, 1961 M. BENTELE ETAL 3,102,492

COMPENSATED ROTARY MECHANISM CONSTRUCTION 6 Sheets-Sheet 5 EROLD F. YCHARLES JONES ATTORNEYS Sept. 3, 1963 M. BENTELE 'ErAL' COMPENSATEDROTARY MECHANISM CONSTRUCTION 6 Sheets-Sheet Filed May 10, 1951 I! I iiII- a? MAX EROLD F. BY CHARLES fly [inf/an, firm 4m A ATTO R N EYS Sept.3, 1963 Filed May 10, 1961 M. BENTELE ETAL 3,102,492

INVENTORS MAX BENTELE EROLD F. PIERCE BY CHARLES JONES #6 1114, Fmywn,ar/MA PM ATTORN EYS p 3, 1963 M. BENTELE ETAL' 3,102,492

COMPENSATED ROTARY MECHANISM CONSTRUCTION Filed May 10, 1961 6Sheets-Sheet 6 INVENTORS' MAX BENTELE EROLD F. PIERCE a BY CHARLES JONESATTOR NEYS United States Patent Office 3,102,492 Patented Sept. 3, 19633,102,492 COMPENSATED scram MECHANISM coNsrnuo'rioN Max Eenteie,Ridgewood, Erold Francis Pierce, Upper This invention relates toimprovements in sealing between working chambers of rotary mechanismsand, more particularly, to improvements in the sealing contact of rotorapex seals to minimize radial movement of the apex seals relative to therotor, especially when a large pressure difference exists across theseal, and to compensate for deviations in seal positions relative to therotor which are caused by deflections and displacements of the rotor,main shaft, and the like from their geometric centers during rotationand also to compensate for deviations in apex seal positions due todistortion of the outer body of the mechanism because of non-uniformtemperature distribution as the rotor rotates relative to the outer bodyduring operations of the mechanism.

Although this invention is applicable and useful in almost any type ofrotary mechanism, such as combustion engines, fluid motors, fluid pumps,compressors, and the like, it is particularly useful in rotatingcombustion engines. To simplify and clarify the explanation of theinvention, the description which follows will, for the most part, berestricted to the use of the inventionin a rotating combustion engine.It will be apparent from the description, however, that with slightmodifications, which would be obvious to a person skilled in the art,the invention is equally applicable to other types of rotary mechanisms.

The present invention is particularly useful in rotating combustionengines of the type which comprise an outer body having an axis,axially-spaced end walls, and a pcripheral wall interconnecting the endwalls, and an inner body or rotor which is mounted within the cavityformed between the inner surfaces of the peripheral wall and the endwalls of the outer body. The inner surface of the peripheral wall ispreferably parallel to the axis of the cavity and, as viewed in a planetransverse to this axis, the inner surface preferably has a multi-lobedprofile which has basically the form of van epitrochoid. The axis of therotor is eccentric from and parallel to the axis of the cavity of theouter body, and the rotor has axiallyspaced end faces disposed adjacentto the end walls of the outer body and a plurality ofcircumferentially-spaced apex portions. The rotor is rotatable relativeto the outer body and its apex portions continuously engage the innersurface of the peripheral wall in gas-sealing contact to form betweenthe outer surface of the rotor and the inner surface of the outer body aplurality of working chambers which vary in volume during engineoperation,

as a result of relative rotation between the rotor and the outer body. 7

Such engines also include an intake passage for administering a fuel-airmixture to the chambers, an exhaust passage for removing burned gasesfrom the chambers, and suitable ignition means so that during engineoperation the working chambers of the engine undergo a cycle ofoperation which includes the four phases of intake, compression,expansion, and exhaust. This cycleof operation is achieved as a resultof the relative rotation between the inner rotor and outer body, and forthis purpose both the inner rotor and outer body may rotate at"different speeds, but preferably the inner rotor rotates while theouter body is stationary.

For efiicient operation of the engine, its working cham- 2 bers shouldbe sealed, and therefore an effective seal is provided between eachrotor apex portion and the inner surface of the peripheral wall of theouter body, as well as between the end faces of the inner rotor and theinner surface of the end walls of the outer body.

Between the apex portions of its outer surface the rotor has a contourwhich permits its rotation relative to the outer body free of mechanicalinterference with the multilobed inner surface of the outer body. Themaximum profile which the outer surface of the rotor can have betweenits apex portions and still be free to rotate without interference isknown as the inner envelope of the multi-lo'bed inner surface and theprofile of the rotor,

proximates this inner envelope.

For purposes of illustration, the following description will be relatedto the present preferred embodiment of the engine in which the innersurface of the outer body is basically a two lobed epitrochoid, and inwhich the rotor or inner body has three apex portions and is generallytriangular in cross-section but has curved or arcuate sides.

It is not intended that the invention be limited, however, to the formin which the inner surface of the outer body is basically a two-lobedepitrochoid and the inner body or rotor has only. three apex portions.In other embodiments of the invention the inner surface of the outerbody may have a different plural number of lobes with a rotor having onemore apex portion than the inner surface or the outer body has lobes.

In generation of the housing or outer body for the rotating combustionengine, it has been the practice .to establish the contour of the innersurface of the outer body by that shape resulting from the initialgeneration of a true epitrochoid having as a generating point the centerof curvature of the tip of the apex seal and adding an amount r equal tothe radius of curvature of the tip of the apex seal normal to the trueepitroclroid over its entire length. This arrangement makes it possibleto use a seal having an arcuate contact surface instead of a pointcontact which would obviously be impractical as an effective sealingmeans between adjacent working chambers of the engine. A furtherdescription of this construction may be found in copending applicationSerial No. 638,127, filed February 4, 1957, now Patent No. 2,988,008.

The resultant contour of the inner surface-of the outer body provides asurface for contact with the apex seal.

tip throughout the entire revolution of the rotor with no radial motionof the seal relative to the rotor notwithstanding the fact that the sealtip has an arcuate surface rather than a point contact. Of course, thislack of radial motion of the seal relative to the rotor can take placeonly if the rotor and main shafts run at their geometric centers at alltimes with no deflection and provided there are no distortions of theinner surface of the housing or outer body due to other causes such astemperature gradients in the outer body.

In operation of the engine, centrifugal forces act on the rotor in amanner which results in movement of the rotor from its geometric centerby an amount substantially equal to the bearing clearances and shaftdeflections in a radial direction away from the axis of the outer bodysubstantially through the rotor axis. If in spite of this shift ordisplacement, and as is necessary for proper sealing, an apex seal is tomaintain contact with the inner surface of the outer body, the seal mustmove radially relative to the rotor. At the major axis the seal mustmove into the rotor and at the minor axis the seal must,

move out of the rotor (there is forced movement of the apex sealrelative to the rotor, since at the major axis of the epitrochoidalinner surface the seal is forced to move 1 into the rotor and at the 'aK factor K such that I tion with the epitrochoidal inner surface, andwhere e is the eccentricity of the rotor axis from the axis of theepitrochoidal inner surface of the outer body. From the equation it isapparent that if R remains constant and e is increased, the K factorofthe epitrochoid must become smaller. a

It is a primary object of the present invention to provide compensatingmeans to partially or fully correct for the effects of centrifugalforces which cause displacements of the rotor from its geometric centerand for distortions caused by temperature gradients. These displacementsand distortions, if not compensated for, result in rclativ radialmovement of the apex seal to the rotor.

This compensating means can be achieved in three ways: 1

1. OUTER BODY COMPENSATION Movement of the rotor from its geometriccenter due to influence of centrifugal forces is equivalent to anincrease in the eccentricity (e) of the rotor axis from the outer bodyaxis. In generating the epitrochoidal inner surface contour of the outerbody, the theoretical eccentricity (e) can be replaced by a new valuee+C or e) where C is a constant equivalent tothe bearing clearances andany necessary additional deflection allowances.

If the radius of the rotor has a design value of R, in

' theory the K factor of the epitrochoidal inner surface to accommodatethe rotor having a radius of R will be but since the bearing clearancesand deflection allowances must be taken into account, the epitrochoidalinner surface is modified to, provide a new epitrochoid which has e+C eThe factor K is sufficiently smaller than the value of I he K called forby the design radius R and design eccentricity e of the epitrochoidalinner surface to restore balance to the equation in spite of the growthof the actual eccentricity to a new value e or e+C. With the newepitrochoid having a K factor K no radial movement of the apex seals isrequired to compensate for shifting of the rotor due to centrifugalforces, bearing clearances and deflection allowances, because the shapeof the epitrochoid itself with a K factor of K compensates fortheshifting.

2. ROTOR ECCENTRICITY CORRECTION Since movement of the rotor from itsgeometric center due to the influence of centrifugal forces isequivalent to an increase'in the eccentricity (e) of the rotor axis fromthe'outer body axis, to a large value (e+C or e), a sec- 0nd means forovercoming the eifects of the centrifugal forces may be achieved byreducing the enlarged eccentricity (e) by replacing the designeccentricity 2 with a new value'e, where e",= =e-C and where C isequivalent to the rotorand shaft bearing clearances and any neces saryadditional deflection allowances and has a magnitude such that eC=e,where e is the original or design eccentricity and e is the enlarged oruncorrected operating eccentricity. Although the R of the rotor remainsthe same, the effective eccentricity e is reduced under this method tothe desired value e by subtracting the amount C from the designeccentricity e during manufacture. With this resultant reducedeccentricity e of the rotor, no radial movement of the apex seals isrequired to compensate for shifting of the rotor due to centrifugalforces because of bearing clearances and other centrifugal deflectionallowances.

' In a sense, reducing the design eccentricity e of the rotor by anamount C provides a compensation for the shift or deflection of therotor from its geometric center which is the inverse of the compensationfor the same problem which is achieved by reducing the K factor or valueof K of the cpitrochoidal inner surface of the outer body to a new valueK which restores balance to the equation i as described under 1 above.

3. COMPENSATION OF RADIUS OF CURVATURE OF CONTACTING SURFACE OF TIPS OFSEAL- ING MEMBERS TION.

By increasing the radius of the curvature of the contacting surface ofthe tips of the sealing members from their design value or the value ofr which is used to create an outer curve parallel to a true epitrochoidand which forms the inner surface, the forced movement of the apexsealing members can be materially reduced in the region of travel on theinner surface in the regions where large pressure differences exist"across the sealing members or apex seals. These large differentialpressures occur substantially between the point where the angle formedbetween the center line of the seal and a perpendicular to the tangentto the curve of the inner surface at its point of contact with thesealing member reaches a maximum and the point where the major axis ofthe epitrochoid intersects the inner surface.

This method of compensating for shifts of the rotor from its geometriccenter under the influence of centrifugal forces not only decreases apexseal movement relative to the rotor in the general region of highdifferential gas pressure across the seals, but also provides anincreased radius of contact between the seal and the inner surface whichbeneficially decreases contact stresses acting against the peripheralwall of the. outer body.

Optionally, an additional correction or modification of the resultantepitrochoid can be made after any of the above-described three ways ofachieving the compensating means have been applied. This additionalcorrection or modification compensates for any distortion of the innersurface of the outer body due to thermal gradients when the engine is inoperation, and the final inner surface contour which results provides amechanical shape that minimiz'cs movement of the apex seals relative tothe rotor.

It is a fundamental object of the present invention to provide means forminimizing relative movement between the apex seal and the rotor duringrevolution of the rotor within the outer body. v

It is another object of this invention to minimize relative movementbetween the apex seal and the rotor by modifying the shape of the innersurface contour to compensate for movement of the rotor from itsgeometric center due to centrifugal forces and by further modifying itsshape to compensate for distortion of the inner surface due to thermalgradients.

It is another object of this invention to minimize relative movementbetween the apex seal and the rotor by re- OR APEX TIP COMPENSA- to thebearing clearances and any additional deflection allowances.

Another object of this invention is to reduce contact stresses of theapex seal against the inner surface of the outer :body by increasing theradius of contact of the seal with the inner surface of the outer body.

A further object of this invention is to improve the sealingcharacteristics of the sealing members by simple and inexpensive changein the radius of curvature of the contacting surface of the tips of thesealing members.

A still further object of the instant invention is to greatly enhancethe scaling properties of the engine through a combination of relativelysmall but important changes in the construction of the engine.

From the foregoing it is apparent that the instant invention is ofoutstanding importance in providing a useful rotating combustion engineby minimizing or practically eliminating relative movement of the apexseals in the rotor during revolution of the rotor inside the outer bodywhen diflferential gas pressure across the seals is high. Obviously, theless the apex seals are required to move in maintaining sealing contactwith the inner surface of the outer body, the more uniform and adequatethe sealing will be.

Broadly described, the instant invention comprises means for minimizingmovement of the apex seals relative to the rotor during rotation of therotor within the outer body. This means comprises modification of theshape of the inner surface contour to compensate for movement of therotor from its geometric center by centrifugal forces during rotation,modifications in the shape of the inner surface contour to compensatefor thermal gradients, reduction of the eccentricity of the rotor tocompensate for movement of the rotor from its geometric center and otherdeflections, and increasing the radius of curvature of the contactingsurface tips of the apex seals from the value used to obtain an outercurve parallel to the basic epitrochoid-al curve used in designing theshape of the outer body cavity.

Additional objects and advantages of the invention will be set forth inpart in the description which follows and in part will be obvious fromthe description, or may be learned by practice of the invention, theobjects and ad vantages being realized and attained by means of theinstrumentalities and combinations particularly pointed out.

in the appended claims.

The invention consists in the novel parts, constructions, arrangements,combinations, and improvements shown and described.

The accompanying drawings which are incorporated in and constitute apart of the specification, illustrate one embodiment of the inventionand, together with the description, serve to explain the principles ofthe invention.

In the accompanying drawings illustrating the mechanical aspects of thepresent inention, it is believed that the showing of the fundamentalconstruction, functions, originality and advantages of the inventionmaybe more easily understood when certain details of practicalconstruction are omitted, where these details form no part of theclaimable invention, are well-known to those skilled in the art, andcould be incorporated in the present invention by any skilled workman.These details may consist of means for lubrication, such as, oil cups,grooves, reservoirs, seals, Wipers, and G-rings; means for reduction offriction, such as, bushings, ball bearings, and roller bearings; meansfor sealing off various spaces or areas to confine fluid pressures totheir functional locale, such as, packing, packing glands, O-rings, andgaskets; constructional details of fluid conducting means, such as, tubeor pipe joints, unions, and

elbows including supporting and securing means; and such othercomparable means and devices that may be omitted for the sake ofclarity.

Of the drawings:

FIG. 1 is a sectional view of the mechanism showing 6 the outer body insection and the rotor positioned for rotation within the outer body;

. FIG. 2 is a central vertical section of the principal portion of theengine showing the rotor within the outer body; FIG. 3 is a diagrammaticview of the mechanism showing the rotor with one apex seal positionedwithin the outer body and also a showing of the rotor (by broken ineand. dot-dash) in two alternate positions. A true epitrochoid is shownby a dot-dash curve which has the center of curvature of the apex sealtip as its generating point; the inner surface cont-our, which isbasically an epitrochoid, appears as a solid line curve and is generatedby adding an amount equal to the apex seal radius normal to the trueepitrochoid over its entire length;

FIG. 4 is a diagrammatic view showing the substantially epitrochoidalinner surface contour of FIG. 3 in a broken line curve, and the innersurface contour after modification to minimize seal movements whichwould otherwise result, for example, from movements of the rotor fromits geometric center due to centrifugal forces, is shown in a solidline. The rotor is shown within the outer body in two positions. In oneposition one of its apex portions is aligned with the major :axis of theouter body and in the other position this apex portion is aligned withits minor axis;

FIG. 5 is a schematic View of the substantially epitrochoidal innersurface of the outer body showing the location of the intake and exhaustports and depicting the amount of heat being rejected per unit areathrough the inner surface into the outer body at various points alongthe inner surface by a broken line curve 2) (A the relative amount oftemperature diiference around the inner surface using the coolest spotas a reference point by dot-dash phantom curce (AT) and the amount ofrelative thermal growth around the inner surface by a double dot-dashphantom curve (AD).

FIG. 6 is a diagrammatic view of the mechanism showing how movement ofthe rotor from its geometric center under centrifugal forces duringrotation maybe come pensated for by reducing the eccentricity of therotor:

FIG. 7 is a diagrammatic view of the profile of the inner surface of theouter body on a plane transverse to the outer body axis. This profile isbasically an epitrochoid; also shown in broken line is an epitrochoidalinner surface which is modified to minimize movement of the sealingmembers relative to the rotor; the intake and exhaust ports are shownschematically, and an outer curve shows the differential pressure acrossan apex seal at all points of location of the apex seal in its travelaround the epitrochoid. An apex is also shown schematically in threedifferent positions of its travel around the epitrochoid.

FIG. 8 is a fragmentary view of an apex seal showing the contactingsurface of the tip of the seal after modification in solid line andbefore modification in broken line.

It is to be understood that both the foregoing general description andthe following detailed description are exemplary and explanatory but arenot restrictive of the invention.

Reference will now be made in detail to the present preferred embodimentof the invention, an example of which is illustrated in' theaccompanying drawings in which FIG. 1 shows a generally triangular rotor10 hav ing arcu-ate sides eccentrically supported for rotation Within anouter body 12 on an axis 14 which is eccentric to and parallel to theaxis 16 of the outer body.

As embodied, the profile of the curved inner surface 18 of the outerbody 12 has a geometric shape which has basically the form of anepitrochoid with two arches lobedefinin-g portions, or lobes. An intakeport 20 is arranged to communicate -with one lobe of the epitrochoidalinner surface 18, and an exhaust port 22 is arranged to cornmunicatewith the other lobe. The center of the epitrochoidal inner surface 18has an axis 16 forming the axis of the outer body 12. There are twopoints of least radius from the center 16 of the epitrochoid-al innersurface 18.. A line connecting these two points of least radius andpassing through the center of the epitrochoid is designated the minoraxis 24 of the epitrochoid. Similarly, the epitrochoid has two pointsof'greatest radius, and a line connecting these two points and passingthrough the center of the epitrochoid is designated the major axis 26 ofthe epitrochoid. i

The epitrochoidal inner surface over a substantial distance adjacent toits major axis describes a concave portion, and describes a convexportion over a lesser distance adjacent its minor axis, as is shown inFIG. 1.

It is apparent that the minor axis 24 divides the epitrochoid into twohalves. For convenience, the half or lobe which communicates with theexhaust port may be designated the exhaust lobe and the half or lobewhich com: municates with the intake port may be designated the intakelobe.

. the axis 16 of the epi-trochoidal inner surface of the outer body. Aneccentric 30 is mounted on the shaft 28 and is coaxial with the rotoraxis 14. The rotor it) is rotatably 'mounted on the eccentric 3t andsuitable counterweights (not shown) are keyed to portions of the shaft28 and serve to counterbalance the eccentric 30 and'the rotor 16 whenthe engine is in operation.

The outer body 12 proper comprises two end walls 32 and 34 and aperipheral wall 36 interconnecting the end .walls. A spark plug 38 ismounted in the peripheral wall 36 and is so disposed that its electrodescommunicate with the working chambers 58 formed in the cavity of theouter body 12 between the inner surface 18 and the outer peripheralsurface of the rotor 10.

The generally triangular rotor has three apex portions 42, two end faces44- and 46 which are disposed adjacent to the end walls 32 and 34 of theouter body 12 (as may be seen in FIG. 2), and three outer peripheralsurfaces or working faces 48 which extend between the end faces 44 and46 of the rotor 10. Each apex portion 42 of the rotor is provided with aslot which extends in an axial direction from one end face 44 to theother 46. An apex sealing member 52 is mounted in each slot 50 and isspring loaded radially outwardly to ensure its continuous gas-sealingengagement with the inner surface 18 of the outer body 12 while theengine is in operation.

An internally-toothed gear 54 is rigidly secured to the rotor 10 at anopening in one of its end faces 44, and an externally-toothed gear orpinion 56 is in turn rigidly secured to one end wall 32 'of the outerbody 12. The teeth of the externally-to-othed gear 56 are in mesh withthe teeth of the internally-toothed gear 54. As embodied, the ratio ofthe intermeshing teeth between the rotor gear 54 and the outer body gear56 is 3:2, so that for every revolution of the rotor about its own axis14 the shaft 28 completes three revolutions in the same direction aboutits axis 16. a

In operation, thus, the rotor 10 performs a planetary rotary movement ina counterclockwise direct-ion with respect to the outer body 12, as maybe seen in FIG. 1. As the rotor lit follows its eccentric path ofrevolution within the outer body 12, the three working chambers 58 ofthe engine vary in volume, and during each complete revolution of therotor each working chamber 58 will undergo the four phases of the enginecycle: intake, compression, expansion, and exhaust. The working chambers58 are isolated from each other by the apex sealing membets 52 which aremaintained in continuous gas-sealing engagement with the inner surface18 of the outer body 12 as the rotor revolves. V

The working faces 43 of the rotor it have channels 60 which are cut intoa substantial area of the working faces 7 i8. These'channels 6t? permitthe hot and burning combustion gases to pass freely from onelobe-defining portion of the outer body 12 to the other, or from theintake lobe to the exhaust lobe and vice versa, when a rotor workingface 48 is in or near the top dead-center compression position, as showninFIG. l. The size and depth of the channel 6% may effectively determinethe compression ratio for the engine.

in FIG. 3 a rotor it} is shown mounted within an epitrochoid 62. Therotor is shown in three different positions 63, 64 and 65. Theepitrochoid 62 is a true epitrochoid, and it may be seen in FIG. 3 thatthe apex portions of the rotor 10 in all three positions illustrated,63, 64,

g and 65, are in point contact, or coincident at their points however,as a practical matter, it would be difficult or I impossible toeffectively seal the working chambers of such an engine from each otherat the sharply pointed vertexes of the apex portions 42 of the rotoriii. A point contact between the rotor apex portions 42 and the trueepitrochoid 62 will thus not yieldan effective seal. Accordingly, anapproximate epitrochoid 66, or curve having basically the form of anepitrochoid, is generated and forms the'actual inner surface 18 of theouter body 12. This approximate epitrochoid 66 is generated by theaddition of a small equal increment of length normal to the trueepitrochoid 62 over its entire length to form, in effect, an outer curve66 parallel to the true epitrochoid 62 over its entire length. The useof an outer parallel curve 66 with a true epitrochoid 62 is described incopending application Serial No. 638,127, filed February 4, 1957, nowPatent No. 2,988,008.

One'sealing member 52 is shown for each rotor position 63 64, and 65 ofFIG. 3.. Each sealing member 52 is curved at its operative end or tip.This curve is generated byradius of curvature for the'contacting surfaceof the apex seal tip. The true epitrochoid 62 is generated by the centerof this apex seal radius r as a generating point as the rotor revolves.Also, as shown in FIG. 3, the equal increment that has been added to thetrue epitrochoid 62 to generate the approximate epitrochoidal innersurface 66 is equal to the length of the apex seal radius r or (seeFIGS. 3 and 8). Accordingly, as the rotor assumes different positionsWithin the epitrochoid 66, it is apparent from FIG. 3 that because ofthe circular curved contact surface of the apex seal 52 and the mannerin which the curve 66 is generated no radial movement of the apex seal52 is required to maintain it in contact with the approximateepitrochoid 66 regardless of the position of the rotor, and that a lineconnecting the center of the apex seal radius with the point of contactwill be normal to the curves 66 and 62 and will intersect them at thepoint of contact and at the center of curvature of the apex seal tipradius respectively, as shown by the lines N and N in FIG. 3.

From the foregoing, it is apparent that if the inner surface 18 of theouter body 12 is designed to conform to the approximate epitrochoid 66of FIG. 3, and if an apex seal having a radius r is used, thedifficulties presented by a point contact of the apex portions 42 withthe true epitrochoid 62 of FIG. 3, can be obviated. Even if the curve ofthe inner surface 18 is theretically perfect, however, the apex sealingmember 52 must nevertheless move to a slight extent with respect to therotor because of centrifugal fields, bearing clearances, shaftdeflections, and thermal distortions.

The eccentricity e of the rotor axis 14 from, the outer body axis 16 isshown in FIG. 3, and the circular path described 'by the rotor center 14as it revolves within the outer body 12 is shown in broken line.

Outer Body Compensation FIG. 4 illustrates one means of achieving theinvention and is briefly described as method 1 above. In general, FIG. 4shows how the epitrochoid 62 (FIG. 3) may have its contour modified toallow for movement of the rotor from its geometric center duringoperation of the engine due to bearing clearances and deflections. Theepitrochoid 62 of FIG. 3 is shown in FIG. 4 by a broken line curve, alsodesignated 62, the modified contour of the epitrochoidal inner surface18 is shown in FIG. 4 as a solid line curve 70. The theoretical orgeometric eccentricity e of the rotor center 14' from the outer bodycenter 16 would describe a solid line circle 72 as shown in FIG. 4 ifthe rotor did not move from its geometric center during operation of theengine. Because of bearing clearances between the bearing bore 74 of therotor and the eccentric 30 upon which the rotor is mounted, otherbearing clearances in the engine, and deflections, the eifect ofcentrifugal force tends to cause the actual eccentricity e to exceed thetheoretical eccentricity e so that the geometric center and center ofgravity CG of the rotor describes the broken line circle 76 rather thanthe solid line circle 72 as rotor It) revolves within the outer body 12.

In FIG. 4, the curve '70, like the curve 62, is a true epitrochoid, andthe seals 52 must have pointed apexes to maintain contact withoutmovement relative to the rotor, as explained above in the description ofFIG. 3. In an actual rotary mechanism, however, the apex seals would beprovided with a rounded apex having a radius of curvature of itscontacting surface equal to the radius r in FIG. 3. Therefore, asexplained in the description of FIG. 3, in a working rotary mechanismwith rounded apex seals, the profile of the inner surface of the outerbody would be a curve similar to the curve 66 of FIG. 3, or a curveparallel to the curve 70 and spaced outward from it by the distance r.No movement of the rounded apex seals relative to the rotor is requiredto maintain contact with such an outer parallel curve. For simplicity indescribing the concept of outer body compensation as depicted in FIG. 4,only the true epitrochoids 62 and 70 are shown. It should be understood,however, that in an actual rotary mechanism the apex seals 52 would berounded, and the profile of the inner surface would be a curve spacedoutward from but parallel to the curve 70.

In FIG. 4 the rotor 10 is shown in two positions: a solid line position78 in which one of its apex seals 52 is aligned with the major axis 26of the modified epitrochoid 70 and a broken line position 80 in whichone of its apex seals 52 is in alignment with the minor axis 24 of themodified or new epitrochoid 70. The effective bearing bore 75 of therotor in the solid line position 78 is shown in solid line as is alsothe eccentric 77 for position 78. The effective bearing bore 79 forrotor position 80 is shown in broken line as is also the eccentric 31for position 80. The centrifugal force acting on the rotor in position78 and its direction is represented by the arrow F 1. Similarly, thecentrifugal force acting on the rotor in position 80 is represented bythe arrow F2.

As can be seen from FIG. 4, the centrifugal force acting on the rotortends to cause all of the bearing clearances to appear on one side ofthe respective eccentrics 77 and 81 and bearing surfaces 75 and 79. Thetotal diametral bearing clearance (2C) between the eccentric and therotor accumulates in the direction along which the centrifugal forces F1and F2 act, as shown by FIG. 4. In FIG. 4, F1 acts along the major axis26, and F2 acts along the minor axis 24, because the centers of gravityCG of the rotors 78 and 80 are coincident with the rotor axes 14, andthe axes of the rotors 78 and 80 (in their positions as shown in FIG. 4)intersect the major axis 26 and minor axis respectively of the epitro-10 choids 62 and 70. Accordingly, when the apex seals 52 are alignedwith the major axis 26 and the minor axis 24 respectively, thecentrifugal force F1 and F2 are also acting in a direction along thesesame axes.

From a study of FIG. 4, it is apparent that the accumulation of totaldiametral bearing clearance (2C) in a radially outward direction fromthe geometric center 16 of the epitrochoid 62 when the apex portion 82of the rotor 78 is aligned with the major axis 26 would tend to forcethe apex seal 52 outside of the epitrochoid 62, if the seal were notfree to move relative to the rotor. Further, when the apex portion 84-of the rotor is aligned with the minor axis 24, it is apparent from FIG.4, that the apex seal 52 would tend to be pulled in, away from theepitrochoid 62, if the apex seal were not forced by appropriate means tomove radially outward relative to the rotor 80.

In view of the foregoing, it is apparent that movement of the apex sealsrelative to the rotor can be minimized by modifying the contour of theepitrochoid 62 and causing it to assume the contour of a modified or newepitrochoid '74 It will be seen from FIG. 4, that the maximum correctionis needed along the major axis 26 and minor axis 24. At each end of themajor axis 26 it will be necessary to add to the major axis of theepitrochoid 62 an incre ment (c) equal to one-half the total bearingclearance, and at each end of the minor axis 24 it will be necessary tosubtract from the length of the minor axis of the epitrochoid 62 theincrement (c) equal to one-half the total bearing clearance. Appropriateintermediate amounts must be added to or subtracted from the epitrochoid62 over its entire length to yield the modified epitrochoid 70 whichwill compensate for the shift of the geometric center of the rotor undercentrifugal force due to hearing clearances. It is obvious that asimilar or further change can be made to allow for any shifts of therotor in the same direction from its geometric center due to clearancesin the bearings for the rotor shaft 28 and due to deflections other thanbearing clearances such as the slight deflection shift caused by theinherent elasticity of the materials from which the engine isconstnucted.

The new epitrochoid 7 0 can be created from the original or designepitrochoid 62 by changing the K factor of the rotating combustionengine. The K factor has previously been described as the value K in theequation where R is the radius or the distance from the rotor axis 14 tothe point of contact of the rotor apex portion with the epitrochoidalinner surface (see FIGS. 1 and 2), and where e is the eccentricity ofthe rotor axis 14 from the central axis 16 of the epitrochoidal innersurface of the outer body. From the equation it is apparent that if Rremains constant and e is increased, the value of K must become smallerif the equation is to remain in balance.

The shift of the rotor from its geometric center by an amount C equal toone-half the total bearing clearance is the equivalent of increasing thedesign eccentricity e of the engine by the amount C. The theoreticaleccentricity e can thus be replaced by a new value e+C or e, where C isequal to the radial bearing clearance and any necessary additionaldeflection allowances. The new epitrochoid 70 is arrived at by designingan epitrochoid which will have a K factor K such that i E K e+C e' The Kfactor of the new epitrochoid 70 will thus be smaller than the K factorof the design epitrochoid 62, or the K factor which is called for by thedesign radius R of the rotor and the design eccentricity e of theengine.

Radial movement of the apex seals which would normally be required tocompensate for shifting of the rotor due to centrifugal forces, bearingclearances and deflection allowances may be virtually eliminated by theuse of the new epitrochoid 7t? with a K factor K. An important featureof this invention is the discovery that a new epitrochoid can be createdwhich will compensate for all centrifugal forces, shifts in rotorposition by the relatively simple expedient of decreasing the design Kfactor, or K, to a new K factor K which can be mathematicallypredetermined from the equation in FIG. shows the amount of heat beingrejected per unit area through the inner surface 18 of the peripheralwall of the outer body at each point along the inner surface 18 oftheepitrochoid 62 (or the epitrochoidfli).

The relative amount of temperature difference around the inner surface18 is shown in FIG. 5 by a dot dash phantom curve (AT) which uses thecoolest spot on the inner surface as a reference point and a double dotdash phantom curve (uDishows the relative amount of thermal growtharound the inner surface 18. The curve AD, however, is greatlyexaggerated for clarity, and the location of the intake port 2% andexhaust port 22 are shown schematically in FIG. 5.

If it were possible to keep the epitrochoidal inner surface 18 at afairly uniform temperature, there would be no need to modify theepitrochoid '70 of FIG. 4 to compensate for distortion of theepitrochoidal inner surface caused by thermal gradients. In practice,however, since 'a perfect cooling system is unattainable, there willalways be some distortion of the epitrochoid 70 due to thermal gradientsin the outer body 12 and this distortion is represented by the curve ADin FlG. 5. It is possible, however, to modify the epitrochoid 7%!)during manufacture so that, although the inner surface will not be atrue epitrochoid when the mechanism is cold, thermal distortions willcause the inner surface to assume the shape of a true epitrochoid atrunning temperatures. This additional modification of the epitrochoidalinner surface can thus virtually eliminate the effect of thermaldistortions at operating temperatures.

. After the epitrochoid 70 has been compensated as described above itshould be still further modified by adding an equal increment outside ofand normal to it over its entire length to form, in efifect, an outercurve parallel to the inner curve over its entire length in the samemannet as previously described in the discussion of FIG. 3.

Rotor Eccentricity Correction A further means by which some of theadvantages of the present invention can be achieved is shown in FIG. 6and was briefly described as method 2 above. In the foregoingdescription relating to FIG. 4 and the means of achieving the results ofthe invention by creation of a new epitrochoid 70', it was explainedthat centrifugal 12 the engine is constructed. The total shift is then acombination of a bearing clearance shift plus the deflection shift andis designated C. v

In FIG. 6, for purposes of clarifying the explanation of this aspect ofthe invention, two positions of the rotor are indicated by a showing oftheir apex portions only. Also, to permit enlargement of the scale ofFIG. 6, instead of showing a complete epitrochoidal inner surface, afragmentary portion of the inner surface comprising slightly morethanone quadrant is shown, but this showing is sufiicient for anunderstanding of the explanation accompanying FIG. 6.

The curve representing the epitrochoidal inner surface in FIG. 6corresponds to the outer parallel curve or approximate epitrochoid 66 ofFIG. 2. Although strictly speaking the approximate epitrochoid 66 is nota true epitrochoid, such as the epitrochoid 62, of FIG. 3, it differsonly slightly from a true epitrochoid and, for practical purposes, inthe ensuing explanation may be considered to be a true epitrochoid. itwill be remembered, that in the description accompanying FIG. 3 it wasexplained that the outer parallel curve for approximate epitrochoid 66was created from the true epitrochoid 62 to permit the use of apex sealswiththe rotor which could have curved tips at their points of contactwith the epitrochoidal inner surface 18, instead of pointed tips havingcontact with the inner surface 18.

sWhen the inner surface of the outer body is a parallel curve, thedistance from the center of the rotor to the parallel curve is onlyslightly greater than the distance to the true epitrochoid on which theparallel curve is based. The difference between these two distances isquite small and has been highly exaggerated in FIG. 3.

Accordingly, since the inner surface 18 of the outer body 12 is aparallel curve to a true epitrochoid, as shown in MG. 3, the K factor ofthe epitrochoid on which the parallel curve inner surface is based issubstantially equal to where R is the distance from the center of therotor to the inner surface and e is the actual eccentricity of the rotorrelative to the axis of the outer body.

As used in this application:

(1) In a true epitrochoid for all practical purposes, where R is thedistance from the center of the rotor to the inner surface of the outerbody.

Also, in this application no distinction will he made between the Kfactor of a true epitrochoid that is determined by the parameters R ande and the K factor (or quasi-K factor) of a parallel curve (66 in FIG.3) that is based on a true epitrochoid. In strict usage, the parallelcurve 66 would not have a K factor per se, since it is not a trueepitrochoid. The parallel curve 66, however, differs so slightly from atrue epitrochoid that for all practical purposes it may be considered tohave a K factor, and this K factor may be stated to be equal to where Ris taken as the distance from the center of the rotor to a point ofsealing engagement at one of its apex portions with the inner surface ofthe outer body.

Again, when a parallel curve is used the radius (R) of the rotor to thepoint of contact with the inner surface will be slightly greater thanthe radius (R) of a rotor used with the true epitrochoid upon which theparallel curve is b ased, because, by definition, the parallel curve isspaced outwardly from the true epitrochoid by the increment r at allpoints.

Accordingly, the radius of the rotor, when a parallel curve is used,would be strictly defined as the R of a rotor for a true epitrochoidplus the increment r. Thus, if R is taken as the radius of the rotor fora true epitrochoid, and R is taken as the radius of the rotor to be usedwith the parallel curve based on the true epitrochoid, the followingrelationship exists: R"=R+r. But the K factor of the parallel curve maystill be represented by because R'=R+r and r is quite small as comparedwith R. Thus and for all practical purposes Accordingly, in the claims,no distinction has been made between either R or R or the K factor ofthe true epitrochoid and the quasi-K factor of the parallel curve As inthe description of FIG. 4, so also in the description of FIG. 6, therotor in position 78 has an apex portion in position 82 along the majoraxis 26 of the epitrochoid 66, and when the rotor is in position 80, ithas its apex portion in position 84 along the minor axis '24 of theepitrochoid 66.

The radially outward shift of the rotor from its geometric center due tothe influence of centrifugal forces is equivalent to an increase in theeccentricity e of the rotor axis from the outer body axis. The shift ofthe rotor causes the design eccentricity e to increase to a larger valuewhich gives the rotary mechanism an actual or effective eccentricitywith a value of (e-l-C) or e, where C is equivalent to the rotor andshaft bearing clearances and any necessary additional deflectionallowances.

With this second principal means of achieving the invention, theenlarged effective eccentricity 6 may be reduced or compensated for by areduction in the original or design eccentricity e of the rotor,although the R of the rotor remains the same. The desired result isachieved by subtracting an amount equivalent to C from the designeccentricity a during manufacture of the rotary mechanism. With thisresultant reduced design eccentricity (e-C) of the rotor, no radialmovement of the apex seals will be necessary to compensate for shiftingof the rotor due to centrifugal forces because of bearing clearances andother centrifugal deflection allowances.

In a sense, reducing the design eccentricity e of the rotor by theamount C provides a compensation for the shift or deflection of therotor from its geometric center which is the inverse of the compensationfor the same problem which is achieved by reducing the value of K or theK 14 factor of the epitrochoidal inner surface of the outer body to anew value K to restore balance to the equation Compensation for rotorshift through reduction of the K factor was described previously in theexplanation of FIG. 4 above.

In both Outer Body Compensation (Means 1, above) and Rotor EccentricityCorrection (Means 2, above), the actual or running eccentricity of theengine (which is the eccentricity that determines the shape of theepitrochoidai inner surface 18 of the outer body 12) is greater than thegeometric eccentricity of the rotor relative to the outer body axis.

In FIG. 6 the uncorrected or basic eccentricity e' is designated by thedot-dash phantom line 86, and the corrected eccentricity (e'-C) or e isshown by the solid line 88, :and the design eccentricity (eC) or e isshown by the broken line 87. The effective bearing bore for the rotor inposition 78 is shown by the dot-dash phantom line 7 5 in its uncorrectedposition, and the position of the eccentric mounted within it isdesignated by the dot-dash phantom line 77. The position of the bearingbore for the rotor in position 78 after correction is shown by the solidline 75 and the position of the eccentric is shown by the solid line 77.

Similarly, the effective bearing bore for the rotor in position 80,before the eccentricity correction has been made, is designated by thedot-dash phantom line 81, and, the position of the eccentric within thisbearing bore is shown by the dot-dash phantom line 79. The position ofthe bearing bore for the rotor in position 80 after correction is shownby the solid line 81, and the position of the eccentric after correctionis shown by the solid line 81, and the position of the eccentric aftercorrection is shown by the solid line 79.

In FIG. 6, the position of the axis and center of gravity of the rotorin position 78, before the eccentricity correction has been made, isdesignated and its position after the eccentricity correction isdesignated 90. Similarly, the position of the axis and center of gravityof the rotor in position 80 before correction is designated 92, and itsposition after correction is designated 92.

From a perusal of FIG. 6 and a study of the way in which the path oftravel of the rotor axis and center of gravity is shifted closer to thecenter of the epitrochoid 66 by the eccentricity correction, and from astudy of the manner in which the bearing clearances are shifted reof therotor in position 80 along the minor axis 24 will be pushed out andtoward the cpitrochoid 66.

When the epitrochoidal inner surface is provided with a designeccentricity of (e-C) or e", the actual or effective eccentricity of theengine will reach the desired value e when the engine is running throughthe addition of the amount C to the design eccentricity (e-C) or e" andwill thus provide exactly the desired effective eccentricity e(e-C,+C=e) or (\e"'+C=e). With this relatively simple change of thedesign eccentricity during manufacture, it is unnecessary to compensatefor rotor shift by modifying the contour of the epitrochoid 62 uponwhich the approximate epitrochoid 66 is based, through a change in its Kfactor. Of course, it may still be necessary to modify the contour ofthe epitrochoid 66 when the method of FIG. 6, is used, to allow fordistortions due to thermal gradients when the engine is at operatingtemper- The apex portion in position 84 is shown in solid line along theminor axis 24 in the position it would occupy after the eccentricitycorrection has been made. This same apex portion is shown in position84' in dot-dash phantom line in the position it would occupy without theeccentricity correction. It canbe seen from FIG. 6, that the apexportion in position 84' is further away 'by the amount C from theepitrochoid 66 than the apex portion in position 84. It should be notedalso that the apex portion in position 84 is the same distance from theepitrochoid 66 as the apex portion in position 82.

In comparing the relative positions of 82 to 82 and 84 to 84, it shouldbe apparent that the apex portion in moving from position 82 to position84 will pull away from the epitrochoid 66 by an amount equal to 2C, ifthe eccentricity correction is not made. When the eccentricitycorrection is made, however, the rotor portion maintains the samedistance away from the epitrochoid 66 in position 82 as in position 84.

An apex seal 52 is shown in solid line, and in section for clarity,within the rotor apex portion in the solid line positions 82 and 84.Similarly, an apex seal 52', is shown in broken line in the rotor apexportion in the phantom line positions 82' and 84'. The broken line apexseal 52' in the rotor posiiton 82' coincides with the solid line apexseal 52, and therefore, is not shown separate from the apex seal 52 inthe drawing of FIG. 6. The two seals 52 and 52 may thus be considered tobe superposed one on the other in FIG. 6. Apex seal 52' is shownrelative to the rotor positions 82 and 84' as it would appear if it didnot move relative to the rotor as the rotor moves from 82' to 84'.

From a study of FIG. 6, it will be apparent that, if effective sealingis to be maintained, without an eccentricity correction, the apex seal52 will have to move through a distance equal to 2C as the rotor movesfrom 82' to 84' to maintain contact with the epitrochoid 66. On theother hand, it is unnecessary for the apex seal 52 (solid line) to moveat all, as the rotor moves from positions 82 to 84. Accordingly,reduction of the design eccentricity during manufacture by an amountequivalent to the rotor shift, offers an effective means of achievingthe Primary desideratum of this invention: to minimize movement of theapex seal relative to the rotor during operation of the rotarymechanism.

When a roller type bearing is used, the above analysis is precisebecause the minimum clearance in such a hearing is always located at thepoint of application of the load on the bearing. FIGS. 1 and 2, however,show a sleeve type bearing. When a sleeve-type bearing (such asillustrated) is used, it is known that the minimum bearing clearance isdisplaced angularly a small amount (in the direction of relativerotation of the rotor with respect to the outer body) from the point ofapplication of the load (centrifugal force) on the rotor to theeccentric. This small angular displacement of the minimum bearingclearance, when a sleeve type bearing is used, may also be taken intoaccount in determining the profile of the epitrochoidal inner surface ofthe outer body.

Apex Seal Tip Compensation FIG. 7 shows the approximate epitrochoid 66(corre sponding to the curve 66 of FIG. 3) in solid line, and the intakeport 20 and exhaust port 22 are diagrammatically or schematicallylocated with respect to this epitrochoid.

The variation of differential gas pressure across an apex seal, or thedifference in gas pressure existing between two adjacent workingchambers of the engine, at all points of travel of the apex seal alongthe entire length of the epitrochoid 62 which represents the innersurface 18 of the outer 'body 12 is shown by a curve of differentialpressure which is designated 93.

FIG. 7 discloses still a third means of achieving the invention. Brieflydescribed, this third means of achieving the invention is throughcompensation of the curvature, or radius of curvature, of the contactingsurface at the tip of the apex seal. For clarity of explanation, onlyone apex seal is shown in FIG. 7 but it is shown in three of thedifferent positions that it assumes as it travels along the innersurface 18 within one quadrant of the epitrochoid 66.

Also shown in broken line in FIG. 7 is the approximate epitrochoid 70'.The epitrochoid 70' corresponds to an outer parallel curve formed fromthe modified epitrochoid 76 of FIG. 4 in the same manner that theapproximate epitrochoid 66 is formed from the epitrochoid 62 in FIG. 3.The apex seal in FIG. 7 is shown greatly exaggerated in size(particularly its width) compared to the epitro'choids 66 and 76. Thissize exaggeration is shown for clarity of explanation only. It will berecalled that the modified epitrochoid 7 0 of FIG. 4 has a K factor,such as K, which has a value smaller than the value K of thetheoretically correct or design K factor of the epitrochoid 62. Themodified epitrochoid 70 with a K factor of K compensates for shifts inposition of the center of the rotor 16, and this method of achieving theinvention has been previously described in the explanation accompany-FIGURE 4. Because the epitrochoid 70' in FIG. 8 is formed from themodified epitrochoid 70 with its K factor K, it compensates for shift ofthe rotor from its geometric center, and the tips of the apex seals ofthe rotor Ill in their paths of travel will exacly follow the innersurface 16 without the necessity for movement relative to the rotor whenthe epitrochoid has the shape of the modified epitrochoid 7 0'.

FIG. 8 is a detail view of the tip of an apex seal. The usual or designconfiguration of the tip is shown in broken line and is designated 94'.A modified tip or a tip with its radius of curvature compensated toachieve the results of the invention is shown in solid line and isdesignated 94. It will be observed that the compensated tip 94 has agreater radius of curvature than the design tip 94. The radius ofcurvature of the compensated tip is designated 95 and the radius ofcurvature of the original or design tip is designated 95'. This latterradius of curvature is equivalent to the value r shown in FIG. 3, whichis the distance by which the outer parallel curve 66 is spaced from thetrue epitrochoid 62.

As stated above, the apex seal in FIG. 7 is shown in section for clarityand is shown in three of the :difle-rent positions that it assumes as ittravels along the inner surface 18.within one quadrant of theepitroichoid 66. As the apex seal proceeds in a counterclockwisedirection from the major axis 26 to a position along the minor axis 24-,the threepositions in turn are designated as 96, 97 and 98. The apexseal which is shown in solid line section in the three positions justdescribed represents an apex seal having a radius of curvature of itstip compensated or modified as shown by 94 in FIG. 8.

Also shown in FIG. 7 in broken line is an apex seal with a design orunmodified radius of curvature, i.e., an apex seal having a radius ofcurvature of its tip which corresponds to the radius of curvature 95 ofthe tip designated 94' in FIG. 8. This apex seal is also shown in threedifferent positions which it assumes in its path of travel along theinner surface 18 from the major axis 26 to the minor axis 24. The tip ofthis latter seal, howpositions assumed by this latter apex seal areshownin broken line :and are designated 96', 97, and 98-to correspond to thethree similar positions of the compensated apex seal in positions-96,97, and 98.

In FIG. 8, it may be seen that the tip of the uncompensated apexseal 94'extends above thetip of the compensated seal 94 by a distance at thecenter of the seal which is equal to C. The amount Chas previously beenV movement of the apex seal relative to the rotor will be defined as anamount equivalent to the increase in ec- .centricity e caused by shiftof the rotor center during op- .eration from its theoretical or designposition, The tip 94 of the apex seal with the compensated radius ofcurvature in position 96 in FIG. 7 will thus be in contactwith theepitrochoid 66, while the tip 94 of the apex seal with .the designradius of curvature in position 96 will be in inner surface 18 towardthe minor axis 24, however, the

angle which its center line forms with a perpendicular to a tangent tothe curve at the point of contact increases from zero to a significantmagnitude until it becomes.

a maximum and then decreases back to zero again when the seal reachesthe'minor axis. The point on the epitrochoidal curve at which the anglebecomes a maximum or the point of maximum lean from the perpendicularap' proximately coincides with the point where the epitrochoid 7intersects the epitrochoid 66 and is represented by the positions 97 and97 of the apex seals, as may be seen in FIG. 7.

, In FIG. 7 the point of contact of the tip of the apex seal with theepitrochoidal inner surface 18 when the seal is at its point of maximumlean from the perpendicular is clesgnated 100 on the inner surface 18.In FIG; 8 the corresponding point of contact on the tip of the apex sealwhen the seal isat its maximum angle of lean from the perpendicular isdesignated 101. It maybe seen in FIG. 8 that both'the modified andunmodifiedor compensated. and uncompensated tips of the apex seals coincide at point 101. i l t a It will be observed in FIG. 7 that with theseals in positions 97 and 97., they are in contactwith the innersurfaces 18 of the epitrochoids 66 and 70' at a point on their tipscorresponding to point 101 of FIG. 8. Since the two epitrochoids 66 and70 also coincide at this point andsince, zbyh mothesis, the broken lineseal or unmoditied seal in moving from position 96' to position. 97.does not move relative to the rotor 10, the modified or compensated sealin moving from position 9 6 to position 97 minimized in the region ofthe epitrochoid quadrant be-- tween the position 96 in which the seal isaligned'with the major axis 26 and the position of maximum seal angu-.1arity with a perpendicular to a tangent to the curve of theepitrochoid 62 at its point of contact with the seal tip. As can be seenfrom FIG. 7 this particular quadrant is on the side of the major axis326 opposite from the side in which the intake port 20 and the exhaustport 22 arelocated, and this quadrant also coincides with the region inwhich differential pressures as represented by curve 93, across an apexseal, or between adjacent work- .ing chambers of the engine, reach theirhighestvalues. 'When the differential pressure across an apex seal is 1high, the gas pressure acting on one side of the seal tends .to' forcethe other side of the seal'into close frictional engagement with theadjacent sideof-the slot 50 in which it is carried by the rotor (seeFIG. 1), and because of this gas pressure force, it becomes difficulttomove the seal relative to the slot 50 when the seal is within thishigh dilterential pressure region. Accordingly, this method of achievingthe invention reduces .seal movement relative to the rotor in thecritical regionof apex seal travel on the epitrochoid 6-2 to. a minimum.a

From a study of FIG. 7, it is apparent that isf the uncompensated orunmodified apex seal tip is used, which in the critical region, apexseal tip compensation through has a radius of curvature approximatelyequivalent to r, or the distance by which the outer. parallel curve 66is separateddrom the epitrochoid 62 in FIG. 3; it will be necessaryforthe apex seal to move outward relative to the rotor 10 in travellingfrom position 96 to position 97,

and it will have to move relative to the rotor by an amountapproximately equal to C.- 1 his movement of the apex seal relative'tothe rotor is required if the unmodified or uncompensated tip of the sealisused with the epitrochoid 66. a a

3 Movement of the apex seal relative IOlhej rotor in the critical regionof travel where differential pressures are high can be almost completelyeliminated by arrelatively simple and inexpensive alteration of theshape or configuration of the tip of the apex seal from a configurationhaving a radius of curvature equal to r to one having a substantiallygreater radius of curvature.

In addition to minimizing movement of the apex seal the use of asubstantially greater radius of curvature for I the tip of the apex sealthan the design radius'of curvalikewise does not move relativeto therotor, for the relative positions of the two seal tips as shown at96 and96' of FIG. 7 (and also as shown in FIG. 8) has not changed in positions97 and 97, i.e., the relative positionsof the two seal tips has beenpreserved in movement of the seal tips from 96 and 96' to 97 and 97'. r

By hypothesis, we know that the iinmodified seal tip has not movedrelative to the rotor in passing .from 9 6' to 97 therefore, since therelative positions of the two seal tips has not changed in moving from96, 96" to 97, 97 themodified seal tip also has not moved relative tothe rotor. I I

As shown in FIG. 8 the seal tips 94and 94 maintain a curvature for only.a portion of the seal width on each side of the centerline 102 of theseal. The remainder of the seal width is faced off by a straight anglecut 103. r

In accordance with the foregoing description and analysis, when thecornpensated or modified tip of the apex seal (94 in FIG. 8) is usedwith the epitr'o choid 66, forced ture provides a further benefit. Thereis an increase radius of seal contact with the inncrlsurface of theouter body which results in decreased contact stresses, since the forcespushing the seal into contact with the inner surface are distributedover a larger area of the inner surface. 6

Both a compensated and an uncompensated apex seal tip are also shown inFIG. 7in positions 98' and 98, respectively, along the minor axis 24- ofthe epitrochoid 66. From a study of positions 98 and'98' in 7 it isapparent that the uncompensated .tip in position 98" is closer to theinner surface of epitrochoid 62 along the niinor axis'24'than isthecompensated tip in position 98. The I compensated tip 98 thus have tomove further relative to the rotor than the uncompensated tip 98' toeffectively seal the engine in the region adjacent the minor axis 24.Accordingly, it is important to provide a force sufiicient to move thecompensated tip radially outward from its position "98 along the minoraxis 24 to a position which will place the tip in contact with theepitro'choid 66. t i i To accomplish this movement an additional force Fmust be applied to the apex seal 98. This force F is normally providedby means, such as a leaf spring, which will i a hold the seal radiallyoutward against the inner surface of the epitrochoid 66. Inhaccordancewith the invention,

in the region of seal travel adjagent the minor axis 24 the innersurfacewhere the lean of the seal way I perpendicular .105 is greatest.

ment relative to the rotorto minimal or insignificant proportions in theregions where 'difierential gas pressure I acrossthe seal is high.Although apex seal tip compensation does not reduce movement of the apexseal in the region adjacent to the minor axis24 to an insignificant Iamount (in fact, it actually increases the amount of moveperpendicularto the tangent to the curve of the epitrochoid 66 at thepoint of contact(see point 100 in FIG. 7)-the differential gas pressure acting acrossthe apex seal is relatively small, and it is insufiicient in magnitudeto seriv apex sealtip with a radius of curvature considerablygreaterthan the theoretical design value r, reduces apex seal move- -ment whichthe apex seal must make to ensure engagement with the epitrochoid inthis region), and although it does not obviate the necessity forsubstantial movement' of the seal relative to the rotor in this region,the

I differential pressure across the seal is small enough, or suff cientlyinsignificant in magnitude, to permit the necessary movement of the scalin this region to be accomplished by the application of a smallsupplementary force F. Apex seal'tip'compensation thus eliminatestheneed for any substantial movement of the seal relative to the rotorin the region where this movement is difficult because of thedifferential gas forces that act on the seal to II tremendouslyincreaseits inertia and resistance to movefmentm Aspreviously'explained, theshape of itheepitrochoidal inner surface of the outer body, or the shapeof the'epitrochoid itself is determined, by the radio between the twovariables-R and e. The variables R and e thus determine the K. factor orthe value of K, that in turn is an index a I of the shape oftheepitrochoid that is generated by a I given R and'afThese sameparameters of the shape of the epitrochoid R, and e, also determine themagnitude of the angle at -(see FIG. "7) formed between the center lineof the'seal and the perpendicular 105 to the epitrochoidinner-surface-18 at the point of contact of the seal with from theeccentric from and parallel to the axis-of the outer body and forplanetary motion about the outer body axis; the rotor having end facesdisposed'adjacent to the end walls and a plurality ofcircumferentially-spaced apex portions, one more in number than thenumber of said lobes with each apex portion substantially tracing saidepitrochoidal inner surface during rotor rotation and beingdisposed insealing engagement with the inner surface of the periphera1 wall to forma plurality of working chambersbetween the rotor and the peripheral wallwhich vary in" volume upon relative rotation of the rotor within theouter body; sealing members at each apex portion of the rotor formaintaining sealing engagement with the inner surface of the peripheralwall, the sealing members being mounted where R is the distance from thecenter of the rotor to a point on the rotor tracing said epitrochoidalinner surface and e is the geometric eccentricity of the rotor axis forthe'axis of the outer body. 7

2. The invention as defined in claim 1, in which said value of K isequal to K, where K is defined as:

v in which R and care defined claim 1, and in which action ofcentnifugal forces. v

3. The invention as defined in claim 2', in which the profile of theinner surface is defined by a curve having basically the formof anepitrochoid but parallel to and In other words, the greater the value ofthe angle'qt the greater is the angle of the lean of the seal away fromthe perpendicular. With these conditions set forth the angle t may bedefined as follows:'

,to the relative movement that is caused by the ,effects of centrifugalfields and the resultant deflections that arelin turn caused by thesefields. The invention provides three means by which the desired resultsmay be achieved during manufacture of the rotary mechanism:

' epitrochoidal inner surface of the outer body;

.(b) Reduction of the design eccentricity of the mech-- anism; and(c)-'Apex seal tipcompensation. I j

The invention in its broader aspects'is not limited to the specificmechansims shown and described but also includes Within the scopeof theaccompanying claims any I departures made from such mechanisms which donot depart from the principles of the invention and which do notsacrifice itschief advantages.

I What is claimed is:

1 A. rotary mechanism'comprising a hollow outer v body having an axis,axially-spaced end walls, and a pcriph'eral wall interconnecting the endwalls, the inner sur- (a) Compensation or modification of the shape ofthe outwardly spaced by an amount equal to 'r from the true epitrochoidhaving a value of K equalto K, the value of r being substantially equalto the radius of curvature of the contacting surface of the tips of thesealing members.

4. The invention as defined in claim 1, in which the shape of the innersurface of the peripheral Wall is modified to counteract radial movementof the sealing members which results from changes 'inthe shape of theinner surface due to thermal gradients.

5. The invention as'defined in claim 1, in which the profile of theinner surface is defined by acurve having basically the form of anepitrochoid but parallel to and outwardly spaced from the trueepitrochoid having a smaller value of .K than that obtained fnom theequation:

in which R and e are defined as in claim 1. II

6. The invention as defined in claim 1, in which the epitrochoidal innersurface of the outer body has two lobes and the inner body has threeapex portions.

7. A rotary mechanism comprising a hollow outer body having an axis,aXially-spacedend walls, and a peripheral wall interconnecting the endwalls, the inner sunface of said peripheral wall having basically theprofile of a multilobed epitrochoid; a rotor mounted within the outerbody fornotation relative to the outer body on an axis eccentricfrom andparallel to the axis of the outer body l and for planetary motion aboutthe outer body axis; the rotor having end faces disposed adjacent to theend walls I and a plurality of circumferentially-spaced apex portions,

one more in number than the number of said lobes with each apex portionsubstantially tracing said epitrochoidal I inner surface-during rotorrotation and being disposed in sealing engagement with the inner surfaceof the peripheral wall to form a plurality of working chambers betweenthe rotor and the peripheral wall which vary in volume upon relativerotation of the rotor within the outer body; sealing members at eachapex portion of the rotor cfior maintaniing sealing engagement with theinner surface of the peripheral wall, the sealing members being mountedfor radial movement in the rotor, said rotor having a geometriceccentricity of its anis from the outer body axis which is less than theeccentricity determining the shape of the epitrochoidal inner surface.

8. The invention as defined in claim 7, in which the shape of the innersurface of the peripheral wall is moditied to counteract radial movementof the sealing members which results from changes in the shape of theinner surface due to thermal gradients,

9. The invention as defined in claim 7, in which said geometriceccentricity of the rotor is less than the eccentricity determining theshape of the epitrochoidal inner surface by the amount that bearingclearances, deflections, and the like displace the center of the rotorradially out- 'ward from its geometric position relative to the outerbody avis because of centrifugal forces on the rotor created duringoperation of the mechanism.

10. The invention as defined in claim 7, in which the profile of theinner surface is defined by a curve having basically the form of anepitrochoid but parallel to and outwardly spaced by an amount equal to rfrom a true epitrochoid, the value of r being substantially equal to theradius of curvature of the contacting surface of the tips of the sealingmembers. i

11. A rotary mechanism comprising a hollow body having an axis,axially-spaced end walls, and a periphery wall interconnecting the endwalls, the inner surface of said peripheral wall having basically theprofile of a multi-lobed epitrochoid; a rotor mounted within outer theouter body for rotation relative to the outer body on an axis ecentricfrom and parallel to the axis of the outer body and for planetary motionabout the outer body axis; the rotor having end faces disposed adjacentto the end walls and a plurality of circumferentially-spaced apexportions, one more in number than the number of said lobes with eachapex portion susbtantially tracing said epitrochoidal inner surfaceduring rotor rotation and being disposed in sealing engagement with theinner surface of the peripheral wall to form a plurality of workingchambers between the rotor and the peripheral wall which vary in volumeupon relative rotation of the rotor within the outer body; sealingmembers at each apex portion of the rotor for maintaining sealingengagement with the inner surface of the peripheral wall, the sealingmembers being mounted for radial movement in the rotor, the profile ofthe epitrochoidal inner surface being defined by a curve havingbasically the form of an epitrochoid but parallel to and outwardlyspaced from a true epitrochoid by a predetermined distance r and inwhich the tip of each seal member engaging the epitrochoidal surface hasa radius of curvature which is substantially greater in magnitude thanthe predetermined amount 1'.

12. The invention as defined in claim 11, in which the radius ofcurvature of the contacting surface of the tips of the sealing membersis sufficiently greater than r to greatly reduce radial movement of thesealing members relative to the rotor in those regions of the innersurface Wankel June 13, 1961 Wankel et a1. June 13,1961

1. A ROTARY MECHANISM COMPRISING A HOLLOW OUTER BODY HAVING AN AXIS,AXIALLY-SPACED END WALLS, AND A PERIPHERAL WALL INTERCONNECTING THE ENDWALLS, THE INNER SURFACE OF SAID PERIPHERAL WALL HAVING BASICALLY THEPROFILE OF A MULTI-LOBED EPITROCHOID; A ROTOR MOUNTED WITHIN THE OUTERBODY FOR ROTATION RELATIVE TO THE OUTER BODY ON AN AXIS ECCENTRIC FROMAND PARALLEL TO THE AXIS OF THE OUTER BODY AND FOR PLANETARY MOTIONABOUT THE OUTER BODY AXIS; THE ROTOR HAVING END FACES DISPOSED ADJACENTTO THE END WALLS AND A PLURALITY OF CIRCUMFERENTIALLY-SPACED APEXPORTIONS, ONE MORE IN NUMBER THAN THE NUMBER OF SAID LOBES WITH EACHAPEX PORTION SUBSTANTIALLY TRACING SAID EPITROCHOIDAL INNER SURFACEDURING ROTOR ROTATION AND BEING DISPOSED IN SEALING ENGAGEMENT WITH THEINNER SURFACE OF THE PERIPHERAL WALL TO FORM A PLURALITY OF WORKINGCHAMBERS BETWEEN THE ROTOR AND THE PERIPHERAL WALL WHICH VARY IN VOLUMEUPON RELATIVE ROTATION OF THE ROTOR WITHIN THE OUTER BODY; SEALINGMEMBERS AT EACH APEX PORTION OF THE ROTOR FOR MAINTAINING SEALINGENGAGEMENT WITH THE INNER SURFACE OF THE PERIPHERAL WALL, THE SEALINGMEMBERS BEING MOUNTED FOR RADIAL MOVEMENT IN THE ROTOR, AND SAIDEPITROCHOIDAL INNER SURFACE HAVING A K FACTOR WHICH IS SMALLER THAN THATCALLED FOR BY THE RELATION